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C₂×#3552 #62745

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• rational
• ambivalent

Aliases

Subgroups

3543 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,6)(7,8)(9,10)(12,17)(13,14)(15,23)(25,26);(4,8)(5,9)(11,12,16,17)(13,19,14,18)(15,20,23,24)(21,26,22,25);(11,13,16,14)(12,18,17,19)(15,21,23,22)(20,25,24,26);(3,5,7,9)(4,6,8,10)(11,14,16,13)(12,19,17,18)(15,22,23,21)(20,26,24,25);(3,6)(4,9)(5,8)(7,10)(11,15)(12,20)(13,21)(14,22)(16,23)(17,24)(18,25)(19,26)

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55733);